Effect of Side-Chain on Conformation of Poly(acrylic acid) - American

Article pubs.acs.org/JPCB

Effect of Side-Chain on Conformation of Poly(acrylic acid) and Its Dielectric Behaviors in Aqueous Solution: Hydrophobic and Hydrogen-Bonding Interactions and Mechanism of Relaxations Jingliang Li and Kongshuang Zhao* College of Chemistry, Beijing Normal University, Beijing 100875, China ABSTRACT: Dielectric behaviors of poly(acrylic acid) (PAA), poly(acrylic acid)-graf t-dodecyl (PAA-g-dodecyl), and poly(acrylic acid)-graf t-poly(ethylene oxide) (PAA-g-PEO) solutions were investigated from 40 Hz to 110 MHz at the solution temperature of 26 °C. For PAA and PAA-g-dodecyl solutions, two dielectric relaxations at about 5 MHz and 150 kHz were observed, whose mechanisms were proved to be the fluctuation of free counterions and condensed counterions, respectively. While for PAA-g-PEO solutions, an extra relaxation around 30 kHz was observed, including the two relaxations just mentioned, and it is related to the hydrogenbonding aggregates in PAA-g-PEO solutions and was attributed to the rotation of the whole molecule. And no relaxation processes caused by dodecyl or PEO side-chains were detected in our measuring frequency range. Based on Mandel’s model, some parameters characterizing the structure of polyelectrolyte chain, such as radius of gyration and Kuhn segment length, were obtained. Both PAA-g-PEO and PAA-g-dodecyl molecules adopt a more compact conformation than PAA, owing to the formation of hydrogen-bonding aggregates and hydrophobic microdomains, respectively. The introduction of dodecyl and PEO side-chains weakens the intramolecular hydrogen-bonding interactions in PAA molecule and makes the flexibility of PAA-g-PEO and PAA-g-dodecyl chains greater than PAA chains. On the other hand, Han10 and Tenhu16 prepared some doublehydrophilic PAA−PEO copolymers, and they found these copolymers can easily form hydrogen-bonding aggregates in water,10,11,16,17 owing to the large number of hydrogen bonds between the carboxyl groups on PAA main-chain and PEO side-chains. The researches of Morishima6,7 and Han9,10 et al. show that hydrophobic or hydrophilic side-chains regulate the interactions in PAA solutions and significantly change the conformation of PAA chain. Thus, it can be considered that modified polyacrylic copolymers exhibit self-assembly properties and great prospects in preparing nanostructures. Additionally, PAA and its modified copolymers are weak polyelectrolytes with many carboxyl groups which partially dissociate in water, leaving PAA main-chain with negative charges (called fixed charge) and ionized hydrogen ions (called counterions) in the bulk solution. The long-range Coulomb repulsion between the fixed charges and the screening of the electrostatic interactions by counterions make the conformation of PAA chain much complex.18,19 Through grafting sidechains, the charge density of PAA main-chain and the hydrophobic interactions can be largely regulated.20 Consequently, the competition between the electrostatic interactions and the hydrophobic/hydrophilic interactions above-

1. INTRODUCTION Hydrophobically modified water-soluble polymers and doublehydrophilic copolymers have attracted considerable attention in both academic studies and industries over the past two decades,1−11 partly because of their potential applications in the field of rheology controlling, oil recovery, flocculation, cosmetics, and pharmacy.1−3 And these copolymers are often treated as models for understanding self-assembly behaviors because they can form aggregates or even polymeric micelles in solution.4−11 Poly(acrylic acid) (PAA) and its derivatives have been used widely in various fields of engineering and technology, such as flocculants and mucoadhesive agents.12 The introduction of side-chains through the carboxyl groups on the PAA chain will change the hydrophobility of PAA chain, regulate intermolecular interactions, and even endow PAA some special functions.13−15 For example, introducing hydrophobic dodecyl side-chains enhances the rheological properties of PAA solution;1,13 grafting hydrophilic poly(ethylene oxide) (PEO) will increase the mucoadhesive properties of PAA,14 which broadens the application of PAA in the biomedical field. Morishima6,7 reported the aggregation behaviors of dodecylmodified PAA copolymers by fluorescence and light scattering and proved that dodecyl side-chains aggregate to form hydrophobic microdomains. Furthermore, the content of dodecyl side-chains largely determined the tendency of these copolymers to undergo intrachain or interchain aggregation.6−8 © 2013 American Chemical Society

Received: May 21, 2013 Revised: August 30, 2013 Published: September 4, 2013 11843

dx.doi.org/10.1021/jp404980h | J. Phys. Chem. B 2013, 117, 11843−11852

The Journal of Physical Chemistry B

Article

Scheme 1. Schematic Illustrations of the Structure of PAA, PAA-g-dodecyl, and PAA-g-PEO Moleculesa

a

The grafted dodecyl and PEO side-chains are randomly distributed on the PAA main-chain.

caused a relaxation located at about 100 MHz. This probably means the frequency of the relaxation originated from sidechains is related to the length of the side-chain. Thus, it is worthwhile to explore whether side-chains of high molecular weight will cause relaxations at a frequency much lower than 100 MHz. The studying of side-chains is one of the core issues in chain dynamics of polyelectrolyte solutions because it can promote the understanding of the conformational behavior of biomacromolecules, as side-chains are often the sites of biological activity.33 To this end, three representative polyelectrolytes were chosen in this work: poly(acrylic acid) (PAA), poly(acrylic acid)-graf t-dodecyl (PAA-g-dodecyl), and poly(acrylic acid)graf t-poly(ethylene oxide) (PAA-g-PEO), whose structures are shown in Scheme 1. Dielectric measurements were carried out on aqueous solutions of these polyelectrolytes from 40 Hz to 110 MHz. Some parameters characterizing the structure of these polyelectrolyte chains, such as radius of gyration and Kuhn segment length, were estimated according to the relaxation parameters obtained by analyzing the dielectric spectra. In the present work, we focused on investigating the effect of hydrophobic or hydrophilic side-chains on the conformation of polyelectrolyte chain and the chain flexibility. Meanwhile, we expect to provide our suggestions on the mechanism of the relaxations occurring in these polyelectrolyte solutions below 100 MHz, especially the relaxation around MHz, and on whether side-chains of high molecular weight will cause relaxation in our measuring frequency range.

mentioned, including between side-chains and between sidechain and main-chain, determines the chain conformation. Exploring how the various interactions affect the conformation of polyelectrolyte chain and the flexibility of the chain will contribute to comprehending the nature of complexity in soft matter systems. In fact, studies about polyelectrolyte solutions have been concentrated on the chain conformation, the distribution of counterions, and the complexes formed by polyelectrolyte for a long time.18,19,21−26 These researches are usually based on the Flory theory and the scaling model,18,21 and they indicate that the polyelectrolyte chain exists in the form of electrostatic blobs and is often described by the necklace-like model.18,19 On the other hand, theoretical researches on the distribution of counterions and their dynamics have also been widely reported.23−26 That is because counterions located around the fixed charges can screen the electrostatic interactions and reduce the effective charge of polyelectrolyte chain, resulting in the changes in chain conformation.18,25 Relatively speaking, experimental research of the polyelectrolyte solution is somewhat backward and is especially insufficient in expounding the chain conformation, chain flexibility, and interactions in the polyelectrolyte solution from the microscopic point of view. It is well know that the dielectric properties of a matter or a system are essentially related to the fluctuation of dipoles and the motions of charges. The frequency-domain dielectric relaxation spectroscopic (DRS), owing to its sensibility to all kinds of polarization, can provide important, sometimes unique information on charge distribution, movements of molecules or ions, and intermolecular interactions.27−34 In fact, the DRS method has been extensively applied to biomacromolecules (DNA, proteins, and poly(amino acid)) and synthesized polyelectrolytes in the past two or three decades and has provided much valuable information including the structures of bound water,27 ion movement,28−30 and dynamics of sidechains.31−33 Nevertheless, the identifications of the mechanism of relaxations in polyelectrolyte solutions in the radio-frequency band are still under controversy, especially the relaxation from a few Hz to 100 MHz. For example, as to the relaxation at around MHz, Mashimo32,33 attributed it to the electrical dipole fluctuations caused by Brownian motion of polyelectrolyte chains, while Ito’s counterion fluctuation theory28−30 argued that the fluctuation of free counterions caused this relaxation. In addition, few studies on the dynamics of side-chains in aqueous solution31−33 reported that the side-chain of small molecular weight (carboxyl groups or amino groups) in poly(amino acid)

2. EXPERIMENTAL SECTION 2.1. Materials. Solid samples of PAA, PAA-g-dodecyl, and PAA-g-PEO were supplied by the group of Prof. Charles C. Han at Chinese Academy of Sciences (Beijing, P. R. China). The procedure of preparing these grafted copolymers and the characterization of their compositions have been reported in recent works of Han.9,10 The weight percent of dodecyl and PEO (Mw: 2.0 × 103 g/mol, determined by 1H NMR measurement and GPC10) side-chains in the copolymers is 10% and 12.93%, respectively, and these two copolymers were named as PAA-g-dodecyl-10% and PAA-g-PEO-13%. Structural details of these copolymers, including molecular weight, weight percent of dodecyl or PEO side-chains, molar ratio of PEO or dodecyl and PAA monomer, are listed in Table 1. PAA, PAA-g-dodecyl-10%, and PAA-g-PEO-13% solid samples (0.5 mg) were first dissolved in 2.0 mL of DMF and then diluted by doubly distilled water (specific resistance higher 11844



Article

determined by equations ε′ = Cs/Cl and κ = Gsε0/Cl, where ε0 is the permittivity of a vacuum. 2.3. Dielectric Analysis. In an applied electric field of frequency f, the dielectric property (permittivity ε and conductivity κ) of an aqueous polyelectrolyte solution can generally be characterized in terms of the complex permittivity ε*:

Table 1. Characteristics of PAA, PAA-g-dodecyl, and PAA-gPEO, Including Molecular Weight (Mw), Weight Percent of Dodecyl or PEO, and Molar Ratio of PEO or Dodecyl and PAA Monomer ( fdodecyl, f PEO)

PAA PAA-g-dodecyl10% PAA-g-PEO-13%

fdodecyl or f PEO (mol %)

dodecyl or PEO (wt %)

Mw (105 g/mol)

4.21

12.93

2.5 2.78

ε* = ε ′ − 0.53

10

2.87

Gs =

Cx(1 + ω 2Lr Cx) + Lr Gx 2 (1 + ω 2Lr Cx)2 + (ωLr Gx)2

− Cr

ε″ = (κ − κl)/ωε0

(1 + ω Lr Cx)2 + (ωLr Gx)2

(4)

The whole dielectric spectrum free of the dc conductivity effect was analyzed using an empirical equation including the Cole−Cole function and the EP term:34,35 ε* = εh +

∑ i

Δεi + Aω−m + jBω−n 1 + (jωτi)αi

(5)

Here Δε (= εl − εh) is the dielectric increment, and εl and εh are the low- and high-frequency limits of permittivity, respectively. τ = 1/2πf 0 is the characteristic relaxation time ( f 0 is the characteristic relaxation frequency) and α (0 < α ≤ 1) the shape parameter indicating the distribution of relaxation time. Aω−m and Bω−n (A, B, m, and n are adjustable parameters) in eq 5 take into account the effect of EP on the real and imaginary part of the permittivity, respectively, on the basis of the power-law frequency dependence method.34,35 In the process of dielectric analysis, first the corrected dielectric loss free of the dc conductivity effect was obtained according to eq 4, where the dc conductivity κl was read out from the conductivity spectra at several kHz. Then it is the important step to eliminate the contribution of electrode polarization from the dielectric spectra. Fitting the eq 5, including two (i = 1, 2) or three (i = 1, 2, 3) Cole−Cole terms and the EP term, to the raw permittivity and the corrected dielectric loss, the EP term (Aω−m and Bω−n) and the raw dielectric parameters were determined. Thus, new ε′ and ε″ curves free of the EP effect were derived by mathematically subtracting the Aω−m from the raw permittivity and the Bω−n

(1)

Gx 2

(3)

Here κl danotes low-frequency limits of conductivity (or called the dc conductivity), ω (=2πf) the angular frequency, and j = (−1)1/2. In the polyelectrolyte solution, usually a considerable electrode polarization (EP) effect dominates at the lowfrequency range. The total dielectric loss contains three parts: the effective dielectric loss of the sample, the dc conductivity contribution, and the contribution of EP. And the contribution of dc conductivity can be subtracted from the conductivity spectra through the equation

than 16 MΩ/cm) to 50 mL with the help of glass rod. Solutions of different concentration from 1.0 to 0.1 mg/mL were obtained, and the pH of all these solutions was adjusted to about 7.0 by the 0.5 mol/L NaOH solution. 2.2. Dielectric Measurements. The complex dielectric permittivity (ε* = ε′ − jε″, where ε′ and ε″ are permittivity and dielectric loss, respectively) of PAA, PAA-g-dodecyl-10%, and PAA-g-PEO-13% solutions was measured by a 4294A Precision Impedance Analyzer (Agilent Technologies), in the frequency range from 40 Hz to 110 MHz, controlled by a personal computer. The applied alternating field was 500 mV, and the measurements were conducted at a constant temperature (299.3 K). A dielectric measuring cell with concentrically cylindrical platinum electrodes was employed to load the samples, the effective area of the electrodes was 78.5 mm2, and the electrode distance was 8 mm. The raw experimental data, capacitance Cx and conductance Gx, were corrected for error from stray capacitance (Cr), the cell constant (Cl), and the residual inductance (Lr), according to Schwan’s method34 based on the following equations: Cs =

⎛ κ ⎞ jκ = ε′ − j ⎜ε″ + l ⎟ ωε0 ωε0 ⎠ ⎝

(2)

where Cs and Gs denote the modified values, respectively. ω (= 2πf, f is the measurement frequency) is the angular frequency. The values of Cl and Cr were determined with pure water, ethanol, and air based on equation the Cx = εCl + Cr, where ε denotes the permittivity of water (ethanol or air) which is known. When plotting the Cx (measured from the impedance analyzer) against ε, a good linear relation will be obtained, then the Cl and Cr were determined, which are 0.480 and 0.109 pF, respectively. The value of Lr was determined by use of standard KCl solutions with different concentrations and the relation Cx = LrGx2. Then the permittivity ε′ and conductivity κ were

Figure 1. Three-dimensional plots of dielectric loss of PAA (a), PAA-g-dodecyl (b), and PAA-g-PEO (c) solutions as functions of the frequency and polyelectrolyte concentration. 11845



Article

Figure 2. Frequency dependence of the permittivity and dielectric loss of PAA (a), PAA-g-dodecyl (b), and PAA-g-PEO solutions (c), all at concentration of 0.5 mg/mL. Black open circles are the raw dielectric data; gray filled circles are the corrected permittivity and dielectric loss after eliminating the effect of electrode polarization (EP) and the dc conductivity, respectively. The solid lines represent the best-fit curves with eq 5.

Table 2. Dielectric Parameters of the Relaxations in PAA, PAA-g-dodecyl, and PAA-g-PEO Solutions with Different Concentrations, Obtained by Fitting Eq 5 to the Dielectric Spectra PAA

PAA-g-dodecyl

c (mg/mL)

Δεl

Δεh

τl (μs)

τh (ns)

αl

αh

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

23.3 24.3 22.9 23.6 21.1 21.0 20.0 20.2 19.9 19.7

12.6 13.2 15.4 14.7 17.7 17.8 18.3 19.1 18.8 18.2

3.89 2.82 1.64 1.54 1.26 1.06 0.851 0.757 0.655 0.604

75.4 58.0 38.6 36.5 32.6 27.9 22.9 19.1 17.1 15.9

0.73 0.71 0.76 0.72 0.81 0.81 0.82 0.81 0.81 0.81

0.76 0.75 0.75 0.75 0.74 0.75 0.76 0.73 0.74 0.75

Δεl 9.12 14.7 15.8 16.7 17.7 16.6 15.6 17.2 16.7 16.4 PAA-g-PEO

Δεh

τl (μs)

τh (ns)

αl

αh

8.21 12.3 14.2 15.6 15.3 17.0 17.2 17.3 17.4 17.3

1.98 2.38 1.81 1.52 1.31 0.775 1.02 0.881 0.791 0.701

91.2 64.3 49.1 39.2 32.8 19.5 27.5 22.3 20.9 18.6

0.78 0.79 0.81 0.81 0.78 0.81 0.84 0.82 0.82 0.86

0.70 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.74

c (mg/mL)

Δεl

Δεm

Δεh

τl (μs)

τm (μs)

τh (ns)

αl

αm

αh

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

16.1 12.5 22.6 29.9 28.5 33.5 31.4 34.1 33.8 33.9

6.52 5.89 6.28 7.69 9.72 9.34 12.3 8.09 11.3 10.3

5.25 8.71 13.3 12.5 15.5 18.1 17.1 20.6 18.8 20.7

9.39 4.08 6.09 5.60 6.46 5.91 6.74 4.32 5.84 3.79

1.01 0.693 0.789 0.572 0.873 0.719 0.753 0.705 0.591 0.476

52.8 64.5 72.7 44.1 47.7 37.3 34.1 32.9 26.5 25.2

0.98 0.98 0.93 0.92 0.94 0.88 0.89 0.83 0.88 0.89

0.90 0.94 0.94 0.94 0.94 0.95 0.94 0.94 0.95 0.94

0.84 0.78 0.70 0.80 0.78 0.77 0.79 0.70 0.74 0.70

solutions, and these relaxations change scarcely with the concentration. But for PAA-g-PEO solutions, the relaxation at low-frequency shows a remarkable dependence on concentration as indicated by the red arrow in Figure 1c, and the dielectric spectra between 100 kHz and 10 MHz presents an unsharp relaxation process that increases obviously with the concentration. In order to identify these relaxation processes more clearly, typical dielectric spectra cut at concentrations of 0.5 mg/mL for the three solutions are shown in Figure 2. Strict analysis of these dielectric spectra was performed according to the method described in section 2.3. The permittivity and dielectric loss of these polyelectrolyte solutions were all well presented by eq 5, as can be seen from the black solid lines in Figure 2. It should be noted in Figure 2 that the EP effect at the low-frequency range (circled by a dashed ring) is well eliminated, and the corrected permittivity (gray filled circles) shows a clear-cut platform of the low-frequency relaxation. Meanwhile, the dielectric parameters of each relaxation were obtained and are listed in Table 2. It can be concluded from Figure 2a,b and Table 2 that there are two dielectric relaxation processes located at around 5 MHz (called high-frequency (HF)

from the corrected dielectric loss, respectively. Finally, the dielectric parameters were determined by simultaneously fitting the Cole−Cole function with the permittivity and dielectric loss after eliminating the EP effect.36 The optimized fitting curves were guaranteed by the nonlinear least-squares method. In this work, parameters m and n were both at about 1.86, which changed little with the concentration of PAA (PAA-g-dodecyl, PAA-g-PEO). Parameters A and B changed largely with the concentration and were on the order of 1011 and 1010, respectively. It was found that at the low frequency range the value of Aω−m dominated the permittivity while the Bω−n was less than 1% of the dielectric loss; these results probably indicate that the EP mainly affects the real part of the permittivity while has little effect on the imaginary part.

3. RESULTS AND DISCUSSION 3.1. Dielectric Spectra and Dielectric Analysis. Figures 1a−c show three-dimensional representations for the concentration dependence of the dielectric spectra for PAA, PAA-gdodecyl, and PAA-g-PEO solutions in the concentration range of 0.1−1.0 mg/mL. It can be clearly seen that there are two or more relaxation processes in PAA and in PAA-g-dodecyl 11846



Article

relaxation) and 150 kHz (low-frequency (LF) relaxation) for PAA and PAA-g-dodecyl solutions, while for PAA-g-PEO solutions, three relaxations were observed at around 5 MHz (high-frequency (HF) relaxation), 200 kHz (middle-frequency (MF) relaxation), and 30 kHz (low-frequency (LF) relaxation), respectively. In addition, for the two relaxations observed in PAA and PAA-g-dodecyl solutions, the shape parameters αl and αh are around 0.80 and 0.75 (see Table 2); the small distributions of these two relaxations probably indicate the heterogeneity in microscopic conformation of the polyelectrolyte chain. The heterogeneity may originate from the distribution of molecular weight (Mw/Mn ≈ 1.4) or from the nonuniformity in the charge distribution on PAA main-chain and in the size of electrostatic blob (or subunit) that describes the microscopic conformation of chains.19,37 And for PAA-g-PEO solutions, both the shape parameters αl and αm are around 0.9, suggesting the spectra of PAA-g-PEO solutions at low-frequency range (10 kHz−1 MHz) results from the partial overlapping of two approximate Debye-like relaxation processes. 3.2. Mandel’s Model and Structural Parameters. There is a general sense in polyelectrolyte solutions that two relaxation processes can be observed below GHz, one at about 1−100 MHz and the other at about 10−500 kHz.28−30 The relaxation at around MHz is usually judged by Ito’s theory28,38 that ascribed this relaxation to the fluctuation of counterions within a correlation length. And the other relaxation at around kHz, which is often hard to detect because the remarkable electrode polarization may obscure the relaxations at low frequency,29 is often attributed to the fluctuation of counterions along the whole chain.38 In the current literature,30,36,39 the mechanisms of the dielectric relaxations in polyelectrolyte solutions were mostly discussed from the viewpoint of counterion fluctuation, suggesting the dielectric behaviors of polyelectrolyte solutions at radio frequency range are mainly determined by counterions. In fact, as early as 1974, Mandel et al.40,41 had proposed a semiquantitative model to describe these two relaxation processes in terms of the fluctuation of counterions along the polyelectrolyte chain. In Mandel’s model, the polyelectrolyte chain is represented as a sequence of charged rod-like subunits in an arbitrary but fixed configuration (as depicted in Figure 3), and the dielectric parameters of the relaxations were combined with conformation of the polyelectrolyte chain. In this work, some conformational parameters, such as the radius of gyration and the length of the subunit of PAA, PAA-g-dodecyl, and PAAg-PEO, can be obtained base on Mandel’s model; thus, the

effect of side-chains on the conformation of PAA can be further discussed. It should be noted that in Mandel’s model the relaxation at around MHz is believed to originate from the local fluctuation of counterions within the subunits. One may find that Mandel’s theory is consistent with Ito’s, for both of them attribute the relaxation to the localized fluctuation of counterions within a certain characteristic length. Thus, Ito’s theory, from this viewpoint, can be considered as an improvement to Mandel’s theory. In this work, Ito’s theory was employed to describe the mechanism of the relaxation around MHz (see section 3.4). According to Mandel’s model,40,41 the dielectric increments of the relaxations caused by the polarization of counterions are given by Δεs =

(ze)2 fNγ (12R g 2 + b2)CM 36kTε0

(6)

Δεh =

(ze)2 fNγ 2 b CM 36kTε0

(7)

where Δεs denotes the static dielectric increment of the solution and Δεh the dielectric increment of the high-frequency relaxation. Rg and b are the radius of gyration and the length of the rod-like subunit (see Figure 3). f is the fraction of counterions tightly bound to the chain, N the total number of counterions per polyelectrolyte molecule (usually equals to the degree of polymerization), ze the charge of a counterion, and γ the ratio of the effective field acting on the polyelectrolyte chain to the average field in the solution. CM denotes the number of polyelectrolyte chains per unit volume and is defined by NCM = 1000αNACp, where CP denotes the molar concentration of monomer, α the ionization degree of carboxyl groups on the chain, and NA the Avogadro’s constant. Substituting Cp into both eqs 6 and 7, the following equations can be obtained: Δεs 1000NA(ze)2 fαγ = [12R g 2 + b2] Cp 36kTε0

(8)

Δεh 1000NA(ze)2 fαγ 2 = b Cp 36kTε0

(9) 41,42

According to Mandel et al., the concentration effect on the dielectric increments can be described by the following empirical equations: (Δεs /Cp)0 Δεs = Cp 1 + Bs Cp

(10)

Δεh (Δε2 /CP)0 = Cp 1 + B2 Cp

(11)

Here, (Δεs/Cp)0 and (Δεh/Cp)0 represent the specific increments extrapolated to infinite dilution. Bs and B2 stand for “interaction parameters” that characterize the interaction strength. It was found that the high-frequency limit of permittivity εh (= 77.7 ± 0.5) in all fitting results of the dielectric spectra was almost the same with the static permittivity of pure water εw (77.9). Therefore, in this work, the static dielectric increment Δεs is equal to the sum of the dielectric increment of each relaxation, namely, Δεs = Δεl + Δεh for PAA and PAA-gdodecyl, and Δεs = Δεl + Δεm + Δεh for PAA-g-PEO (see from

Figure 3. A schematic diagram of the conformation of polyelectrolyte chain in solution. The polyelectrolyte chain is represented as a sequence of charged rod-like subunits. b denotes the length of the rodlike subunit. The radius of gyration of the chain Rg2 = (1/n)∑ni=1(Ri − Rcm)2, where n is the number of the rod-like subunit and Rcm is the vector of the mass center. 11847



Article

derived in Mandel’s model40,41 are strictly valid only at infinite dilution because this model ignores the counterion−counterion interaction as well as the contribution of the permanent dipole moment of the polyelectrolyte to the polarization. Thus, the structural parameters obtained in this study can only be used semiquantitatively to describe the conformation of polyelectrolyte chain and the chain flexibility. 3.3. Effects of Hydrophobic/Hydrophilic Interaction on the Chain Conformation and Chain Flexibility. It can be seen from the structural parameters in Table 3 that Rg of PAA-g-dodecyl and PAA-g-PEO molecules, which reflects the molecular dimension, is about 1/5 of that of PAA, indicating PAA-g-dodecyl and PAA-g-PEO adopt a more compact conformation than PAA. As a weak polyelectrolyte, there are plenty of un-ionized carboxyl groups and a few carboxylate ions on PAA main-chain; the conformation of the PAA chain is mainly determined by the large number of intramolecular hydrogen-bonding interactions. When some hydrophobic or hydrophilic side chains are grafted onto the PAA chain, the hydrogen-bonding interactions will be replaced partly by the hydrophobic/hydrophilic interaction between the grafted sidechains, resulting in the change in molecular conformation. In PAA-g-dodecyl solutions, hydrophobic dodecyl side-chains will aggregate to form hydrophobic microdomains driven by hydrophobic interaction.5−8 In fact, Morishima6,7 and Han9 have demonstrated that PAA-g-dodecyl molecules self-assemble to form aggregates in water by fluorescence and light scattering. Therefore, it can be deduced that the convergence of dodecyl side-chains toward the hydrophobic microdomains will causes PAA main-chain to shrink toward the microdomains, leading to the significant reduction in molecular dimension of PAA-gdodecyl molecules. As to PAA-g-PEO, many researches have proved this kind of copolymer to form hydrogen-bonding aggregates in water,10,16,17 owing to the hydrogen-bonding interactions between the carboxyl groups on PAA main-chain and PEO side-chains throughout PAA-g-PEO molecules. It means that in PAA-g-PEO solutions a part of the PAA mainchain will draw near to PEO side-chains so that carboxyl groups can form hydrogen bonds with EO units. Therefore, the molecular dimension of PAA-g-PEO is much smaller than that of PAA. The molecular dimensions of the three polyelectrolytes and their conformation in aqueous solution are schematically shown in Figure 5.

Table 2). The ratios of Cp/Δεh and Cp/Δεs are plotted as a function of Cp in Figure 4 according to the eqs 10 and 11 (the molar concentration of monomer Cp is converted from the concentration c in mg/mL).

Figure 4. Plots of Cp/Δεs and Cp/Δεh against Cp for PAA, PAA-gdodecyl and PAA-g-PEO solutions.

It can be seen from Figure 4 that for the three polyelectrolyte solutions Cp/Δεh (or Cp/Δεs) shows linear relationships with Cp, from which parameters (Δεs/Cp)0, (Δεh/Cp)0, Bs, and B2 were obtained, and these values are listed in Table 3. Then, Table 3. Structural Parameters for PAA, PAA-g-dodecyl, and PAA-g-PEO Solutionsa Bs (10−3 L/mol) Bh (10−2 L/mol) (Δεs/Cp)0 (10−5 L/mol) (Δεh/Cp)0 (10−4 L/mol) b0 (nm) ⟨Rg⟩0 (nm) L0 (nm) bk (nm)

PAA

PAA-g-dodecyl

PAA-g-PEO

20.1 7.39 7.75 1.52 60.7 123 434 5.91

1.41 6.42 0.511 1.27 55.6 27.8 112 1.16

0.373 1.76 0.237 0.531 35.8 22.2 84.9 0.967

radius of gyration ⟨Rg⟩0, length of the rod-like subunit b0, chain contour length L0, chain flexibility bk, specific increments extrapolated to infinite dilution (Δεs/CP)0 and (Δε2/CP)0, and “interaction parameters” Bs and Bh. a

substituting (Δεs/Cp)0 and (Δεh/Cp)0 into eqs 8 and 9, ⟨Rg⟩0 and b0 can be calculated. However, it is very difficult to evaluate the value of γ theoretically and experimentally; here the γ was taken as 1 because it does not differ too much from unity.41 f = h/lB (Bjerrum length lB = e2/4πεwkBT equals 0.717 nm in this work) was estimated from Manning’s theory of counterion condensation.43 h = 0.252/α is the average distance between charged groups on PAA main-chain (0.252 nm is the average distance on fully ionized PAA chains44). Thus, it is easy to get the equation fα = 0.252/lB. Therefore, the values of ⟨Rg⟩0 and b0 for these polyelectrolytes were calculated from eqs 8 and 9, and the values are listed in Table 3. Additionally, as polyelectrolyte chains will employ a rather stretched conformation at infinite dilution, the chain contour length L0 can be estimated by L0 = 12⟨Rg⟩02 + b02, and the Kuhn segmental length bk, which evaluates the flexibility of a polymer chain, was calculated according to the equation bk = limN′→∞(⟨R2⟩/N′b) = ⟨Rg2⟩0/ 6L0. The calculated results of L0 and bk are also listed in Table 3. It should be mentioned here that the theoretical expressions

Figure 5. Schematic illustrations of conformation of PAA, PAA-gdodecyl, and PAA-g-PEO molecules.

It can be further concluded from above results that hydrophobic dodecyl or hydrophilic PEO side-chains greatly regulated the hydrophobic and hydrogen-bonding interactions in PAA solutions and significantly changed the conformation of PAA chain. Furthermore, the introducing of dodecyl or PEO side-chains will also changes the flexibility of PAA chains. Generally, the larger the size of polymer “coils”, i.e., the bigger the molecular dimensions, the smaller the flexibility of 11848



Article

(here lB and h are the Bjerrum length and average distance, respectively, as stated earlier in section 3.2). In this work, lB = 0.717 nm is much larger than h (h < 0.5 nm20,44), which means part of the counterions will “condense” in the vicinity of fixed charges; these counterions are called “condensed counterions” which are tightly bound by fixed charges. Other counterions are loosely bounded by the screened electrostatic potential owing to the shielding effect of the condensed counterions and sparsely distributed in a wide range between the chains; these counterions here are called “free counterions” because they are much free compared with condensed counterions. Figure 6

polymer chains. From another structural parameter, the Kuhn segment length bk, the flexibility of the chain can be evaluated quantitatively, and the chain with bigger flexibility has a shorter Kuhn segment. It can be seen from Table 3 that the values of bk for these polyelectrolyte chains are 5.91 nm (for PAA), 1.16 nm (PAA-g-dodecyl), and 0.967 nm (PAA-g-PEO), indicating the order of flexibility: PAA-g-PEO ≈ PAA-g-dodecyl ≫ PAA. It is well know that the flexibility of a polymer chain is related to the changes in chain conformation. On the other hand, the structure of a polymer chain determines the difficulty in conformational change and in chain internal rotation, which immediately affects the flexibility of polymer chain. Since the main-chain of these three polyelectrolytes are all PAA and the grafting contents of side-chains are small (see Scheme 1 and Table 1), the effects of dodecyl or PEO side-chains on the flexibility of PAA chain are mainly through changing the strength of intramolecular interactions. This judgment can be supported by the “interaction parameter” Bs in Table 3 that the intramolecular interactions are obviously stronger in PAA than in PAA-g-dodecyl and PAA-g-PEO solutions. The stronger the intramolecular interaction will result in a smaller flexibility of the chain because the chain internal rotation suffers greater restriction. This result provides evidence for the above judgment on the order of chain flexibility. From above analysis, it can be seen easily that the chain flexibility of graft copolymers is closely related to the properties of the side-chain. To understand better the order of flexibility of these polyelectrolytes, a more detailed explanation is as follows: in PAA-g-dodecyl solutions, the aggregation of dodecyl sidechains draws PAA main-chain near to the hydrophobic microdomains, as described in the discussions at the beginning of this section, which leads to a partial break of the hydrogen bonds between the carboxyl groups on PAA chain. On the other hand, grafting dodecyl side-chains will decrease the number of carboxyl groups, so that the hydrogen-bonding interaction within PAA chain was further reduced. Therefore, the partial destruction of hydrogen bonds on PAA main-chain endows PAA-g-dodecyl chains more flexibility. As to PAA-gPEO solutions, some carboxyl−carboxyl hydrogen bonds on PAA main-chain were destroyed, and part of these broken carboxyl groups formed new and relatively weaker hydrogen bonds with EO units. Thus, the intramolecular hydrogenbonding interaction is weaker in PAA-g-PEO than in PAA solutions, resulting in a greater flexibility of PAA-g-PEO chains. 3.4. The Mechanism of the Relaxations. As described in section 3.1, two relaxations at around 5 MHz and 150 kHz for both PAA and PAA-g-dodecyl solutions while three relaxations for PAA-g-PEO solutions were observed. Namely, there is a new relaxation at around 30 kHz in PAA-g-PEO solutions except the two relaxations above. In order to distinguish clearly the mechanisms of these relaxations, especially the mechanism of the extra relaxation around 30 kHz in PAA-g-PEO and the controversial relaxation around MHz in these solutions, it is necessary to gain more understanding into the features of these polyelectrolytes. PAA, PAA-g-dodecyl, and PAA-g-PEO are all polyacids; the ionization of carboxyl groups leaves negative charges (fixed charges) on PAA main-chain and hydrogen ions (counterions) in bulk solution. The pH of these polyelectrolyte solutions was adjusted to about 7.0 by NaOH solution, so that most of hydrogen ions were neutralized and the counterions in solution were mainly Na+. According to Manning’s counterion condensation model,43 the counterions in polyelectrolyte solution will condense near the fixed charges when lB/h > 1

Figure 6. Distribution and the fluctuation of free counterions (○) and condensed counterions (gray circle) in the polyelectrolyte solution. The condensed counterions fluctuate along the chain within the distance equals to the chain contour length L; the free counterions, trapped by the screened electrostatic potential ψ, fluctuate perpendicular to the polyelectrolyte chain within the distance ξ.

schematically shows the distribution of counterions and the fluctuation of free and condensed counterions under electric field. The condensed counterions are tightly bound by fixed charges, and they fluctuate along the chain backbone within the distance equals to the chain contour length L. The free counterions are loosely constrained by the screened electrostatic potential owing to the shielding effect of the condensed counterions, and they fluctuate perpendicular to the polyelectrolyte chain within the distance ξ. To examine the relaxation mechanisms in detail, we plotted in Figure 7 the reciprocal of the relaxation time of each relaxation (1/τi) against the molar concentration of the polyelectrolyte (Cp), according to the relaxation times in Table 2 obtained from analyzing the dielectric spectra. It was found that 1/τi shows linear relationships with Cp which can be described by the following empirical equations proposed by Mandel et al.41,42

Figure 7. Plots of 1/τi against Cp for PAA, PAA-g-dodecyl, and PAA-gPEO solutions. 11849


The Journal of Physical Chemistry B τi = (τi)0 /(1 + BCp)

Article

s45) and replacing the fluctuation distance ξ with the length of subunit b0 in Table 3, and these values are also listed in Table 4. It can be seen from Table 4 that for PAA, PAA-g-dodecyl, and PAA-g-PEO solutions the extrapolated relaxation times of high-frequency relaxations (τh)0 are very approximate to the theoretical values of the fluctuation of free counterions (τfree)0 calculated from eq 13, suggesting the high-frequency relaxation (around 5 MHz) in these polyelectrolyte solutions all originates from the fluctuation of free counterions. Moreover, the diffusion coefficients of sodium ion DNa+ for the three solutions were estimated from eq 15. In the calculation, the average charge distance h in eq 15 was first determined to be 0.313 nm by the relation h = 0.252/α; here the ionization degree α = 0.799 was obtained by putting pH = 7.0 and pKa = 6.420,44 into equation pH = pKa + log[α/(1 − α)].20 Next, the diffusion coefficient DNa+ was calculated by substituting h and the dielectric increments Δεh and the relaxation time τh of the highfrequency relaxations (from Table 3) into eq 15. The values of DNa+ in these solutions change scarcely with the polyelectrolyte concentration, and the mean values are 0.984 × 10−9 (in PAA solutions), 0.858 × 10−9 (PAA-g-dodecyl), and 0.708 × 10−9 m2/s (PAA-g-PEO), respectively. All these values are close to 1.33 × 10−9 m2/s, the diffusion coefficient of Na+ in water,45 indicating the Na+ free counterions in these polyelectrolyte solutions exhibit strong abilities of diffusion and can move much freely. This result also gives support to the conclusion that the high-frequency relaxations in PAA, PAA-g-dodecyl, and PAA-g-PEO solutions are caused by the fluctuation of free counterions. As to the relaxation arise from the fluctuation of condensed counterions, the relaxation time τcond can be obtained by the equation29

(12)

i (= l, m, h) is the number of relaxation process and B a constant. The relaxation time at infinite dilution, (τi)0, for these three solutions were obtained by extrapolating Cp to zero, and these values are listed in Table 4. It is interesting to note that in Table 4. Relaxation Times of Each Relaxation at Infinite Dilution and the Theoretical Relaxation Times Calculated from the Theory of the Fluctuation of Counterions, Namely, Eqs 13 and 16 PAA

PAA-g-dodecyl

experimental valuesa 1.68 × 10−5 0.605 × 10−5

(τl)0/s (τm)0/s (τh)0/s

1.64 × 10−7 theoretical 3.96 × 10−5 4.60 × 10−7

(τcond)0/s (τfree)0/s

1.57 × 10−7 predictions 0.261 × 10−5 3.85 × 10−7

PAA-g-PEO 1.05 × 10−5 1.07 × 10−6 1.42 × 10−7 1.52 × 10−6 1.59 × 10−7

a Not from analyzing the dielectric spectra directly, but from the 1/τi ∼ Cp lines in Figure 7.

Figure 2 the relaxation time of the MF relaxation for PAA-gPEO is close to that of the LF relaxations for PAA and PAA-gdodecyl, while the corresponding relaxation times in Table 4 show some differences. It should be noted that the relaxation times in Table 4 were at infinite diluted solution where intermolecular interactions can be neglected. However, for PAA-g-PEO solutions, the hydrogen bonds between PAA and PEO significantly strengthen the intermolecular interactions as the concentration increases.10,16 Thus, the differences between Figure 2 and Table 2, we think, may originate from the different effects of concentration on the relaxation time for PAA, PAA-gdodecyl, and PAA-g-PEO (as indicated in Figure 7). On the other hand, in polyelectrolyte solutions, the relaxation around kHz is often ascribed to the fluctuation of condensed counterions;29,36,38,39 the other relaxation between 1 and 100 MHz is attributed to the fluctuation of free counterions by more and more studies30,36,39 based on Ito’s theory of counterion fluctuation.28 As to the relaxation arise from the fluctuation of free counterions, the relaxation time τfree is determined by the fluctuation distance ξ of the free counterions and the diffusion coefficient Df ree, according to Ito’s theory:28−30 τfree ≈

ξ2 6Dfree

τcond ≈

(13)

(14)

where concentration cn denotes the number density of monomers, h the average distance, and εm the permittivity of water. Combining eq 13 with eq 14, the diffusion coefficient Dfree can be obtained:

Dfree =

Δεfree 6τfreehεmcn

(16)

where L is the fluctuation distance of condensed counterions that equals to the chain contour length (see from Figure 6), and ζ is the friction coefficient of condensed counterions moving along the polyelectrolyte backbone.29 Substituting the values of L0 in Table 3 and the friction coefficient of Na+ counterions ζNa+ (= 5.2 × 10−12 kg/s)46 into eq 16, the relaxation times of the fluctuation of condensed counterions at infinite dilution, (τcond)0, were calculated, and the results are also listed in Table 4. For PAA and PAA-g-dodecyl solutions, the relaxation times of LF relaxations extrapolated to infinite dilution, (τl)0, approximately equal to the theoretical values, (τcond)0, calculated from eq 16. While for PAA-g-PEO solutions, the relaxation time of MF relaxations (τm)0 (= 1.07 × 10−6 s) matches with the calculated (τcond)0 (= 1.51 × 10−6 s). These results demonstrate that the LF relaxations (around 150 kHz) in both PAA and PAA-g-dodecyl solutions and the MF relaxation (around 200 kHz) in PAA-g-PEO solutions are caused by the fluctuation of condensed counterions. It can also be seen from Figure 7 that the relaxation time of the MF relaxation in PAA-g-PEO solutions showed similar behaviors (the slope of the 1/τi ∼ Cp lines) with that of the LF relaxation in PAA and PAA-g-dodecyl solutions; this result gives support to the above conclusion. It can also be found in Figure 7 that for these three systems both the slopes of 1/τh ∼ Cp and 1/τl ∼ Cp lines (1/τm for PAA-gPEO) show the same order: PAA-g-PEO ≈ PAA-g-dodecyl < PAA, which indicates that the dielectric behaviors of PAA-gPEO deviate partly from PAA; this may be explained by the fact

And the dielectric increment Δεfree is given by Δεfree ≈ hεmcnξ 2

ζL2 6kBT

(15)

According to eq 13, the theoretical relaxation times (τfree)0 of the fluctuation of free counterions for these three polyelectrolyte solutions were calculated by substituting into the diffusion coefficient of Na+ in water (which is 1.33 × 10−9 m2/ 11850



Article

parameters obtained from analyzing the dielectric spectra. It was found that PAA-g-PEO and PAA-g-dodecyl molecules adopt a more compact conformation than PAA. This was interpreted by the hydrophobic and hydrogen-bonding interactions concerned with dodecyl and PEO side-chains: In PAA-g-dodecyl solutions, dodecyl side-chains aggregate to form hydrophobic microdomains; and in PAA-g-PEO solutions, the hydrogen-bonding interactions between the carboxyl groups and PEO side-chains lead to the forming of hydrogen-bonding aggregates. Furthermore, the order of chain flexibility of these polyelectrolytes was evaluated to be PAA-g-PEO ≈ PAA-gdodecyl ≫ AA. That is because the existence of dodecyl and PEO side-chains partly breaks the carboxyl−carboxyl hydrogen bonds within PAA molecule, which weakens the intramolecular interactions in PAA-g-dodecyl and PAA-g-PEO molecules. As a result, the PAA-g-dodecyl and PAA-g-PEO chain shows a greater flexibility than PAA because the chain internal rotation suffers smaller restriction. This study illustrates the effects of hydrophobic/hydrophilic side-chains on the conformation of the polyelectrolyte chain and the chain flexibility by the DRS method. The findings in this work may contribute to comprehending the nature of the complexity in soft matter systems and will also provide new insights for understanding the dielectric behaviors of the polyelectrolyte solution containing side-chains.

that the hydrogen bonds between PAA and PEO significantly affect the intermolecular interactions in PAA-g-PEO solutions.10,16 Additionally, it can be found from Figure 7 that the LF relaxation (around 30 kHz) in PAA-g-PEO solutions behave differently from that in PAA and PAA-g-dodecyl solutions, suggesting the LF relaxation in PAA-g-PEO solutions probably originate from other mechanisms, except the fluctuation of condensed counterions. Generally, the low-frequency relaxation in macromolecular solutions is attributed to the rotation of the whole molecule.38,47 In the case of PAA-g-PEO solutions where the polyelectrolyte chains exist in the form of hydrogenbonding aggregates,10,16 the conformation of PAA-g-PEO molecules can be approximately viewed as spherical particles. Under this hypothesis, the rotational relaxation τrot of PAA-gPEO molecules can be estimated by the Stokes−Einstein− Debye (SED) theory:47,48

τrot =

4πRH 3η kBT

(17)

where RH denotes the hydrodynamic radius, kBT the thermal energy, and η the solvent viscosity. In the dilute solution of PAA-g-PEO, the hydrodynamic radius of intramolecular aggregates RH was about 15 nm, which was obtained through the dynamic light scattering experiment; details can be seen in Han’s published work.10 Taking η = 0.837 × 10−3 N s/m2,49 the rotational relaxation time at infinite dilution was estimated to be 0.874 × 10−5 s; this calculated value is very close to 1.05 × 10−5 s, the extrapolated relaxation time of the LF relaxation in PAA-g-PEO solutions (see Table 4). This finding confirms the above speculation that the low-frequency relaxation in PAA-gPEO solutions is caused by the rotation of the whole PAA-gPEO molecule. As discussed above, the mechanisms of the relaxations observed in PAA, PAA-g-dodecyl, and PAA-g-PEO solutions within the radio-frequency band have all been identified. Meanwhile, it can be further deduced that no relaxation processes caused by dodecyl or PEO side-chains were detected in this work. This probably indicates that there is no relation between the position of the relaxation frequency caused by side-chains and the molecular weight of the side-chain.

■

AUTHOR INFORMATION

Corresponding Author

*Phone +86010-58808283; e-mail [email protected] (K.Z.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

REFERENCES

The authors thank Dr. Jin-kun Hao (The Institute of Chemistry, The Chinese Academy of Science, China) and Prof. Chi Wu (Department of Chemistry, The Chinese University of Hong Kong, Hong Kong) for supplying the sample used in this experiment. The financial support from the National Natural Scientific Foundation of China (No. 21173025, 20976015) and the Major Research Plan of NSFC (No.21233003) is gratefully acknowledged.

4. CONCLUDING REMARKS Dielectric behaviors of PAA, PAA-g-dodecyl,and PAA-g-PEO solutions with concentrations from 0.1 to 1.0 mg/mL at a constant temperature were investigated in the frequency range of 40 Hz−110 MHz. After removing the effect of electrode polarization successfully, two relaxations at around 5 MHz and 150 kHz were observed in PAA and PAA-g-dodecyl solutions, whose mechanisms were ascribed to the fluctuation of free and condensed counterions, respectively, via Ito’s counterion fluctuation theory. While for PAA-g-PEO solutions, a new relaxation at around 30 kHz was confirmed besides the two relaxations above; this extra relaxation is related to the hydrogen-bonding aggregates in PAA-g-PEO solutions and was attributed to the rotation of the whole molecule. These findings support Ito’s counterion fluctuation theory in which the relaxations at around MHz and kHz in the polyelectrolyte solution are identified as the fluctuation of counterions. Some parameters characterizing the structure of polyelectrolyte, such as radius of gyration and Kuhn segmental length, were obtained based on Mandel’s model by using the dielectric

(1) Candau, F.; Selb, J. Hydrophobically-modified polyacrylamides prepared by micellar polymerization. Adv. Colloid Interface Sci. 1999, 79, 149−172. (2) Winnik, M. A.; Yekta, A. Associative polymers in aqueous solution. Curr. Opin. Colloid Interface Sci. 1997, 2, 424−436. (3) Kataoka, K.; Harada, A.; Nagasaki, Y. Block copolymer micelles for drug delivery: design, characterization and biological significance. Adv. Drug Delivery Rev. 2001, 47, 113−131. (4) Chen, J. Y.; Jiang, M.; Zhang, Y. X.; Zhou, H. Characterization of unimolecular micelles of random copolymers of sodium 2(acrylamido)-2-methylpropanesulfonate and methacrylamides bearing bulky hydrophobic substituents. Macromolecules 1999, 32, 4861−4866. (5) Morishima, Y.; Nomura, S.; Ikeda, T.; Seki, M.; Kamachi, M. Macromolecules 1995, 28, 2874−2881. (6) Noda, T.; Morishima, Y. Hydrophobic association of random copolymers of sodium 2-(acrylamido)-2-methylpropanesulfonate and dodecyl methacrylate in water as studied by fluorescence and dynamic light scattering. Macromolecules 1999, 32, 4631−4640. (7) Sato, Y.; Hashidzume, A.; Morishima, Y. Self-association in water of copolymers of acrylic acid and N-dodecylmethacrylamide as studied

11851



Article

by fluorescence, dynamic light scattering, and rheological techniques. Macromolecules 2001, 34, 6121−6130. (8) McCormick, C. L.; Middleton, J. C.; Cummins, D. F. Watersoluble copolymers. 37. Synthesis and characterization of responsive hydrophobically modified polyelectrolytes. Macromolecules 1992, 25, 1201−1206. (9) Hao, J. K.; Li, Z. Y.; Cheng, H.; Wu, C.; Han, C. C. Kinetically driven intra-and interchain association of hydrophobically and hydrophilically modified poly(acrylic acid) in dilute aqueous solutions. Macromolecules 2010, 43, 9534−9540. (10) Hao, J. K.; Yuan, G. C.; He, W. D.; Cheng, H.; Han, C. C.; Wu, C. Interchain hydrogen-bonding-induced association of poly(acrylic acid)-graft-poly(ethylene oxide) in water. Macromolecules 2010, 43, 2002−2008. (11) Holappa, S.; Kantonen, L.; Winnik, F. M.; Tenh, H. Selfcomplexation of poly(ethylene oxide)-block-poly(methacrylic acid) studied by fluorescence spectroscopy. Macromolecules 2004, 37, 7008− 7018. (12) Rabiee, A. Acrylamide-based anionic polyelectrolytes and their applications: A survey. J. Vinyl Addit. Technol. 2010, 16, 111−119. (13) Mylonas, Y.; Bokias, G.; Iliopoulos, I.; Staikos, G. Design of poly(ethylene glycol)-tethered copolymers as novel mucoadhesive drug delivery systems. Eur. Polym. J. 2006, 42, 849−857. (14) Serra, L.; Doménech, J.; Peppas, N. A. Eur. J. Pharm. Biopharm. 2006, 63, 11−18. (15) Wang, X. X.; Qiu, X. P.; Wu, C. Comparison of the coil-toglobule and the globule-to-coil transitions of a single poly(Nisopropylacrylamide) homopolymer chain in water. Macromolecules 1998, 31, 2972−2976. (16) Holappa, S.; Karesoja, M.; Shan, J.; Tenhu, H. Solution properties of linear and branched block copolymers consisting of acidic and PEO blocks. Macromolecules 2002, 35, 4733−4738. (17) Khousakoun, E.; Gohy, J. F.; Jerome, R. Self-association of double-hydrophilic copolymers of acrylic acid and poly(ethylene oxide) macromonomer. Polymer 2004, 45, 8303−8310. (18) Barrat, J. L.; Joanny, J. F. Theory of polyelectrolyte solutions. Adv. Chem. Phys. 1996, 94, 1−66. (19) Dobrynin, A. V.; Rubinstein, M. Prog. Polym. Sci. 2005, 30, 1049−1118. (20) Laguecir, A.; Ulrich, S.; Labille, J.; Fatin-Rouge, N.; Stoll, S.; Buffle, J. Eur. Polym. J. 2006, 42, 1135−1144. (21) Odijk, T. Possible scaling relations for semidilute polyelectrolyte solutions. Macromolecules 1979, 12, 688. (22) Thunemann, A. F.; Müller, M.; Dautzenberg, H.; Joanny, J. F.; Löwne, H. Polyelectrolyte complexes. Adv. Polym. Sci. 2004, 166, 113− 71. (23) Kłos, J.; Pakula, T. Lattice Monte Carlo simulations of a charged polymer chain effect of valence and concentration of the added salt. J. Chem. Phys. 2005, 122, 134908. (24) Carnal, F.; Stoll, S. Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations. J. Phys. Chem. A 2012, 116, 6600−6608. (25) Prabhu, V. M. Counterion structure and dynamics in polyelectrolyte solutions. Curr. Opin. Colloid Interface Sci. 2005, 10, 2−8. (26) Lo, T. S.; Khusid, B.; Koplik, J. Dynamical clustering of counterions on flexible polyelectrolytes. Phys. Rev. Lett. 2008, 100, 128301. (27) Nandi, N.; Bhattacharyya, K.; Bagchi, B. Dielectric relaxation and solvation dynamics of water in complex chemical and biological systems. Chem. Rev. 2000, 100, 2013−2045. (28) Ito, K.; Yagi, A.; Ookubo, N.; Hayakawa, R. Crossover behavior in high-frequency dielectric relaxation of linear polyions in dilute and semidilute solutions. Macromolecules 1990, 23, 857−862. (29) Bordi, F.; Cametti, C.; Colby, R. H. Dielectric spectroscopy and conductivity of polyelectrolyte solutions. J. Phys.: Condens. Matter 2004, 16, 1423−1463.

(30) Cametti, C.; Zuzzi, S. Radiowave dielectric properties of sodium maleate copolymers in aqueous solutions in light of a scaling approach. J. Phys. Chem. B 2010, 114, 7140−7147. (31) Bordi, F.; Cametti, C.; Paradossi, G. Side-chain dynamics in poly(α-glutamate) and poly(γ-glutamate) aqueous solutions: a highfrequency dielectric investigation. Phys. Chem. Chem. Phys. 1999, 1, 1555−1561. (32) Mashimo, S.; Ota, T.; Shinyashiki, N. Dielectric study on chain dynamics of poly(glutamic acid) in aqueous solution using the frequency range 107−1010 Hz. Macromolecules 1989, 22, 1285−1288. (33) Mashimo, S.; Miura, N.; Shinyashiki, N.; Ota, T. Dielectric study on molecular motions of poly(glutamic acid) in aqueous solution over a frequency range of 105−1010 Hz. Macromolecules 1993, 26, 6859− 6863. (34) Schwan, H. P. Determination of Biological Impedances; Physical Techniques in Biological Research; Nastuk, W. L., Ed.; Academic Press: New York, 1963; Vol. VIB, pp 3 23−407. (35) Stoneman, M. R.; Kosempa, M.; Gregory, W. D.; Gregory, C. W.; Marx, J. J.; Mikkelson, W.; Tjoe, J.; Raicu, V. Correction of electrode polarization contributions to the dielectric properties of normal and cancerous breast tissues at audio/radiofrequencies. Phys. Med. Biol. 2007, 52, 6589−6604. (36) Liu, C. Y.; Zhao, K. S. Dielectric relaxations in chitosan solution with varying concentration and temperature: analysis coupled with a scaling approach and thermodynamical functions. Soft Matter 2010, 6, 2742−2750. (37) Liao, Q.; Dobrynin, A. V.; Rubinstein, M. Molecular dynamics simulations of polyelectrolyte solutions: nonuniform stretching of chains and scaling behavior. Macromolecules 2003, 36, 3386−3398. (38) Ookubo, N.; Hirai, Y.; Ito, K.; Hayakawa, R. Anisotropic counterion polarizations and their dynamics in aqueous polyelectrolytes as studied by frequency-domain electric birefringence relaxation spectroscopy. Macromolecules 1989, 22, 1359−1366. (39) Vuletić, T.; Babić, S. D.; Ivek, T.; Grgičin, D.; Tomić, S.; Podgornik, R. Structure and dynamics of hyaluronic acid semidilute solutions: a dielectric spectroscopy study. Phys. Rev. E 2010, 82, 011922. (40) Van der Touw, F.; Mandel, M. Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules: I. Theory. Biophys. Chem. 1974, 2, 218−230. (41) Van der Touw, F.; Mandel, M. Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules: II. Experimental results with synthetic polyelectrolytes. Biophys. Chem. 1974, 2, 231−241. (42) Mandel, M.; Odijk, T. Dielectric properties of polyelectrolyte solutions. Annu. Rev. Phys. Chem. 1984, 35, 75−108. (43) Manning, G. S. Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties. J. Chem. Phys. 1969, 51, 924−933. (44) Mylonas, Y.; Staikos, G.; Ullner, M. Chain conformation and intermolecular interaction of partially neutralized poly(acrylic acid) in dilute aqueous solutions. Polymer 1999, 40, 6841−6847. (45) Longsworth, L. Temperature dependence of diffusion in aqueous solutions. J. Phys. Chem. 1954, 58, 770−773. (46) Koneshan, S.; Lynden-Bell, R. M.; Rasaiah, J. C. Friction coefficients of ions in aqueous solution at 25 °C. J. Am. Chem. Soc. 1998, 120, 12041−12050. (47) Cametti, C.; Marchetti, S.; Gambi, C. M. C.; Onori, G. Dielectric relaxation spectroscopy of lysozyme aqueous solutions: Analysis of the δ-dispersion and the contribution of the hydration water. J. Phys. Chem. B 2011, 115, 7144−7153. (48) Koenderink, G. H.; Zhang, H. Y.; Aarts, D. G. A. L.; Lettinga, M. P.; Philipse, A. P.; Nägele, G. On the validity of Stokes−Einstein− Debye relations for rotational diffusion in colloidal suspensions. Faraday Discuss. 2003, 123, 335−354. (49) Korson, L.; Drost-Hansen, W.; Millero, F. J. Viscosity of water at various temperatures. J. Phys. Chem. 1969, 73, 34−39.

11852


Effect of Side-Chain on Conformation of Poly(acrylic acid) - American

Recommend Documents